A growing amount of observational and theoretical evidence suggests that most main sequence stars are surrounded by disks of cometary material. The dust production by comets in such disks is investigated when the central stars evolve up the red giant and asymptotic giant branch (AGB). Once released, the dust is ablated and accelerated by the gas outflow and the fragments become the seeds necessary for condensation of the gas. The origin of the requisite seeds has presented a well known problem for classical nucleation theory. This model is consistent with the dust production observed in M giants and supergiants (which have increasing luminosities) and the fact that earlier supergiants and most WR stars (whose luminosities are unchanging) do not have significant dust clouds even though they have significant stellar winds. Another consequence of the model is that the spatial distribution of the dust does not, in general, coincide with that of the gas outflow, in contrast to the conventional condensation model. A further prediction is that the condensation radius is greater that that predicted by conventional theory which is in agreement with IR interferometry measurements of alpha-Ori.